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As said in the title, I have a French residence permit and I would like to know if I need a UK visa if I transit there?

Thank you!

The UK government has an excellent tool(click here) to see if you need a visa. I did a check on a citizenship that usually requires a visa to transit in the UK and will not be leaving the airport.

Exemptions

You don’t need a visa if you have one of the following:

• a visa for Canada, New Zealand, Australia or the USA (this can be used
  for travel to any country)


• a residence permit issued by Australia or
  New Zealand


• 
  a common format residence permit issued by an European
  Economic Area (EEA) country or Switzerland


• a resident permit issued by
  Canada after 28 June 2002


• a uniform format category D visa for entry
  into a country in the European Economic Area (EEA) or Switzerland


• an
  Irish biometric visa (marked ‘BC’ or ‘BC BIVS’ in the ‘Remarks’
  section)


• a Schengen Approved Destination Scheme (ADS) group tourism
  visa where the holder is travelling to the Schengen country that
  issued the visa


• a flight ticket from the Schengen area, if you can
  prove that you entered the Schengen area in the previous 30 days on
  the basis of a valid Schengen ADS visa


• a valid USA I-551 Temporary
  Immigrant visa issued by the USA (a wet-ink stamp version will not be
  accepted)


• a valid USA permanent residence card issued by the USA on or
  after 21 April 1998


• an expired USA I-551 Permanent Residence card
  issued by the USA on or after 21 April 1998, with a valid I-797 letter
  authorising extension


• a valid standalone US Immigration Form 155A/155B
  issued by the USA (attached to a sealed brown envelope) All visas and
  residence permits must be valid.

I have highlighted in bold the one that would apply to you. Please check with your own nationality and circumstances to be sure on the link provided.